Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation

• URL: http://arxiv.org/abs/2602.20304v1
• Date: Mon, 23 Feb 2026 19:34:47 GMT
• Title: Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation
• Abstract summary: An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation.<n>A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern.<n>We propose a framework designed from the ground up with these goals in mind.
• Score: 32.9796391255775
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation: representing the volume of intersection between two colliding geometries via a discrete set of properly distributed contact points. A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern, and thus rely on logic and control flow that hinder these goals. We instead propose a framework designed from the ground up with these goals in mind, by trying to strike a middle ground between: i) convex primitive based approaches used by common robotics simulators (efficient but not differentiable), and ii) mollified vertex-face and edge-edge unsigned distance-based approaches used by barrier methods (differentiable but inefficient). Concretely, we propose: i) a representative set of smooth analytical signed distance primitives to implement vertex-face collisions, and ii) a novel differentiable edge-edge collision routine that can provide signed distances and signed contact normals. The proposed framework is evaluated via a set of didactic experiments and benchmarked against the collision detection routine of the well-established Mujoco XLA framework, where we observe a significant speedup. Supplementary videos can be found at https://github.com/bekeronur/contax, where a reference implementation in JAX will also be made available at the conclusion of the review process.

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